Thomas Y. He, Kathy Q. Ji, Alice X. H. Zhao
Published 2020-01-01Version 1
The main objective of this paper is to prove Bressoud's conjecture for $j=0$. The case for $j=1$ has been recently proved by Kim. We first obtain an overpartition analogue of Bressoud's conjecture for $j=1$ by using a bijective method. We then show that Bressoud's conjecture for $j=0$ can be derived from the overpartition analogue of Bressoud's conjecture for $j=1$ with the aid of the relation between the partition function $B_0$ in Bressoud's conjecture and the partition function $\bar{B}_1$ established in our previous paper.
Overpartitions and Bressoud's conjecture, I
The Rogers-Ramanujan-Gordon Theorem for Overpartitions
An Overpartition Analogue of Bressoud's Theorem of Rogers-Ramanujan Type
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